Classifying weak Fano toric varieties of Picard rank $3$

Zhengning Hu; Rohan Joshi

Classifying weak Fano toric varieties of Picard rank $3$

Algebraic Geometry 2025-06-03 v1

Authors: Zhengning Hu , Rohan Joshi

Abstract

We provide a systematic method to classify all smooth weak Fano toric varieties of Picard rank $3$ in any dimension using Macaulay2, and describe the classification explicitly in dimensions $3$ and $4$ . There are $28$ and $114$ isomorphism classes of rank $3$ weak Fano toric threefolds and fourfolds, respectively.

Keywords

weak Fano toric variety Picard rank Macaulay2 classification algebraic geometry

Cite

@article{arxiv.2506.00715,
  title  = {Classifying weak Fano toric varieties of Picard rank $3$},
  author = {Zhengning Hu and Rohan Joshi},
  journal= {arXiv preprint arXiv:2506.00715},
  year   = {2025}
}

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